Republicans and Democrats are skirmishing over President Barack Obama’s health care law this week, and the fight is expected to intensify with the Supreme Court hearing arguments over the law’s constitutionality starting next week.

The battle is part of an underlying war — the presidential campaign — and top Republicans hope to leverage the attention on the 2-year-old law for maximum political effect.

In the House, Republicans are bringing up a bill this week to eliminate a cost-control panel created in the law.

Meanwhile, the National Republican Congressional Committee is targeting Democrats with a “Remember Repeal?” campaign that highlights their votes against repealing the law at the beginning of the 112th Congress.

Republicans will have other chances to take shots at the law, including when Congress considers other health-care-related legislation, such as reauthorization of the Prescription Drug User Fee Act.

Later this summer — when the Supreme Court is expected to rule — will provide another opportunity to highlight the issue.

The Republican presidential frontrunner, former Massachusetts Gov. Mitt Romney, has focused primarily on the economy. He might not be the best messenger for a GOP attack on the law, as the Massachusetts health care law he helped craft and signed is a model for the federal law.

But Congressional Republicans, who uniformly opposed the federal law, appear to be ramping up their criticism of the president’s signature domestic policy achievement.

Senate Minority Leader Mitch McConnell (Ky.), for instance, recently told the Weekly Standard that “Obamacare should be the No. 1 issue in the campaign.”

Republicans, or at least the top Republicans’ spokesmen, see the health care law as a natural extension of talking about the economy.

Health care and the economy are “inexorably linked,” said Don Stewart, a spokesman for McConnell. “Obamacare is a big part of the reason the American people are still asking, ‘Where are the jobs?’” said Michael Steel, a spokesman for Speaker John Boehner (R-Ohio).

Still, several Republicans said privately that the pivot is a hedge against what was previously the party’s focus on the unemployment rate.

That rate is currently at 8.3 percent and has been at 8 percent or above for virtually all of Obama’s term. In the past six months, the rate has gone from 9.1 percent to 8.3 percent.

Some GOP officials marvel that Obama hasn’t been hurt more by unemployment and, more broadly, the pace of the recovery.

“You can make the point that 8.3 percent is a long way from the 6 percent that they said unemployment would be at this time if we voted for the stimulus package. I think that’s a legitimate comment,” Sen. John McCain (R-Ariz.) said.

But if unemployment continues to improve before Election Day, it could help Obama politically.

Complicating the issue is the question of which GOP nominee will be delivering the political message.

GOP House aides said preparations to coordinate with the eventual nominee have been stuck in limbo as the long primary is playing out. The message and approach would be different for Romney than it would for former Sen. Rick Santorum (Pa.), these sources say.

For some Republicans, there are plenty of topics for the GOP to pick up on.

Asked what would be the pivotal issue of the presidential campaign, Sen. Scott Brown (R-Mass.) said, “Well, it’s a few. It’s not just one. It’s really about debt, deficit, taxes, spending, jobs, national security. It’s about energy policy — or lack thereof. It’s about the high cost of energy, it’s about the unemployment rates — people wanting to have jobs and can’t, people have given up. And regulatory and tax certainty.”

And when it comes to health care, Democrats say Romney’s ability to criticize the federal health care law is hampered by his involvement in the Massachusetts law.

“Mitt Romney makes it basically impossible for Republicans to effectively use health care as a message in the fall. His health care reform law was the basis for the national health care law,” said Bill Burton, a senior strategist at Priorities USA, a super PAC that supports Obama.

Romney, who has vowed to repeal the federal law, has disputed the extent to which his law was the basis for Obama’s.

“He does me the great favor of saying that I was the inspiration of his plan. If that’s the case, why didn’t you call me?” Romney said in April.

With the upcoming Supreme Court review and anniversary, Obama and fellow Democrats are planning their own messaging campaign.

“Democrats will have a strong coordinated message emphasizing the personal stories of everyday Americans who have benefited already from the law and would suffer if Republicans had their way and repeal went into effect,” a senior House Democratic aide said. This aide added that the administration, Congressional Democrats and outside groups are planning events, videos and online efforts.

The goal for Democrats is to focus on the individual benefits of the law.

“When you look at every individual element of the health care law, people are wildly in favor of it,” Burton said. “In fact, I would say, if anybody brings up health care in this election, it will probably be Democrats, because this is something we can be on offense on and not just in a defensive crouch as a result of some broad poll number.”

On a conference call with reporters Monday, Rep. Doris Matsui (D-Calif.) referred to a constituent, “L,” who “spends over $600 a month on prescription drugs ... thanks to the [president’s health care] law, ‘L’ will save over $1,000 this year alone on prescription drug costs.”

For Democrats, a Supreme Court decision declaring all or parts of the bill unconstitutional would seem to be a worst-case scenario heading into the fall.

Burton said, “I think the Supreme Court can be an unpredictable place. We’ll take a look at the decision and respond appropriately. I think it’s hard to know exactly what will happen or what the appropriate response will be.”